- Title
- Enumerations of vertex orders of almost Moore digraphs with selfrepeats
- Creator
- Baskoro, Edy; Cholily, Yus Mochamad; Miller, Mirka
- Date
- 2008
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/70067
- Identifier
- vital:100
- Identifier
-
https://doi.org/10.1016/j.disc.2007.03.035
- Identifier
- ISSN:0012-365X
- Abstract
- An almost Moore digraph G of degree d > 1, diameter k > 1 is a diregular digraph with the number of vertices one less than the Moore bound. If G is an almost Moore digraph, then for each vertex u ∈ V (G) there exists a vertex v ∈ V (G), called repeat of u and denoted by r (u) = v, such that there are two walks of length ≤ k from u to v. The smallest positive integer p such that the composition rp (u) = u is called the order of u. If the order of u is 1 then u is called a selfrepeat. It is known that if G is an almost Moore digraph of diameter k ≥ 3 then G contains exactly k selfrepeats or none. In this paper, we propose an exact formula for the number of all vertex orders in an almost Moore digraph G containing selfrepeats, based on the vertex orders of the out-neighbours of any selfrepeat vertex. © 2007 Elsevier B.V. All rights reserved.; C1
- Publisher
- Elsevier
- Relation
- Discrete Mathematics Vol. 308, no. 1 (2008), p. 123-128
- Rights
- Copyright Elsevier
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; Almost Moore digraph; Integer programming; Number theory; Numerical methods; Problem solving; Selfrepeats; Vertex orders; Graph theory
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